Estimation of Demand for Wheat by Classes for the United States and the European Union

This study estimates demand for wheat differentiated by classes using a dynamic AIDS model for the United States and the European Union (EU). The results suggest that imported wheat is more price responsive than domestic wheat in the U.S. market but not in the EU market. The high price responsiveness of Canadian wheat in the U.S. market may suggest that the Canadian policy that reduces prices in the U.S. market or U.S. export subsidies that raise prices of U.S. wheat could be expected to give rise to substantial substitution of Canadian for U.S. wheat. ESTIMATION OF DEMAND FOR WHEAT BY CLASSES FOR THE UNITED STATES AND THE EUROPEAN UNION The world wheat market is one of the most widely studied commodity markets (McCalla 1986; Alaouze, Watson, and Sturgess 1978; Wilson, Koo, and Carter 1990; and many others). These studies have shown that the world market for wheat is extremely complex and includes imperfectly competitive elements stemming from market structure (large grain trading companies and state importers), the heterogeneity of the product and its many end uses, and the extensive intervention of governments in both exporting and importing countries. In North America and Europe, wheat is a very important commodity both because of its central place in food consumption patterns in these regions and because of its importance as a source of farm income. Given these diverse considerations, it is not surprising that wheat has been at the heart of trade disputes (the Canada-U.S. dispute over durum wheat) and policy conflicts (the U.S. and EU export subsidy competition). The objective of this study is to estimate demand functions for wheat differentiated both by country of origin and end uses for the United States and the EU. These estimates provide important information for understanding substitutability among different types and classes of wheat, including domestic wheat. They are particularly informative for these countries, where multiple classes of domestic and imported wheat are consumed. For example, U.S. wheat millers purchase various classes of domestic wheat in addition to two major types imported from Canada. Similarly, in the EU domestically produced common and durum wheat, as well as imports of various types of wheat from the United States and Canada, are consumed. Substitution possibilities among or between domestic and imported wheat are extremely important in understanding wheat import demand and the potential impact of particular trade policies. For example, an understanding of the substitutability between U.S. and Canadian 2 durum in the U.S. domestic market is critical for analyzing wheat-related conflicts between these two countries. Differentiation of wheat both by country of origin and by end uses has been analyzed by many researchers including Laurel (1991); and Wilson (1989). Laure found that the assumption of one form of product differentiation or the other would be appropriate if countries specialize in one product type and the given product type is exported by only one country. In the case of wheat, this is not applicable because most countries trade more than one class of wheat. Sumner, Alston, and Gray (1994) argued that differentiation of wheat is clearly evident from the fact that particular countries both export and import wheat. According to Sumner, Alston, and Gray, if the goods are perfect substitutes, exports and imports would not coexist except in marginal border trade where one region of a country imports and another region of the same country exports. Most previous studies have assumed perfect substitutability across classes and origins. Some studies allow imperfect substitutability of wheat of different origins. However, most of these studies assume perfect substitutability among wheat classes originating from the same source country. For this study, wheat is also differentiated into three categories according to end uses. The three primary industrial uses of wheat include pasta made from durum wheat; bread from hard spring wheats and, to a lesser extent, hard red winter wheats, which have the ideal physical configuration; and other milling products such as pastries and crackers, which can be made from hard red winter, soft, and white wheat. Within each category, wheat from one national region is differentiated from another region. For example, Canadian durum is an imperfect substitute for U.S. durum or durum from any other origin. One reason that has been 3 suggested for differentiating wheat by country of origin is that countries have different policies and these policies make the sales conditions different from one country to another. Substitutability between durum and spring or other wheat is not allowed in the demand estimation because there are limited technical substitution possibilities between durum and spring or other wheat (Alston, Gray, and Sumner 1994). Theoretical Considerations in Modeling Demand Functions A traditional approach to identify price response in international trade is to employ the elasticity of substitution model. In this approach, logarithms of relative import ratios are regressed on logarithms of income and relative prices. The functional form used in the specification has been criticized because it is not derivable from an underlying model of optimization behavior. Another specification, the Armington model, also has been widely used in modeling trade flows of differentiated commodities. The Armington approach distinguishes imports by country of origin and uses a two-step procedure for the import decision. The model has been criticized because of its restrictive assumption that the elasticity of substitution is constant and equal across pairs of commodities (Alston, et. al. 1990). According to Grennes, Johnson, and Thursby (1977) a naive constant share model has yielded superior predictions relative to the Armington model for heterogeneous commodities like wheat. The Almost Ideal Demand System (AIDS) developed by Deaton and Muellbauer (1980), an alternative specification derived from demand theory, has also been widely used in demand analysis. The model has been used to analyze import behavior with respect to aggregated wheat by Hennings and Martin (1987). This study assumed product differentiation among classes but aggregated wheat of similar classes with different origins (i.e., U.S. durum was aggregated with 4 Canadian durum, U.S. hard red spring with Canadian western red spring wheat). More recently, Wilson (1994) used translog demand functions derived from dual relationships to estimate demand for wheat classes by Pacific Rim countries. The translog demand function used by Wilson is similar to the AIDS specification, except for the inclusion of a second-order logarithmic term for the expenditure variable. Using this approach, Wilson concluded that it may be inappropriate to allow differentiation by origin but found perfect substitutability across classes exported from a particularly country. The different specifications used in previous studies to represent wheat demand are static in nature. Static demand specifications are unlikely to capture the behavior of consuming regions because it take time to adjust fully to any changes in market conditions, including price changes. Several factors account for this slow adjustment on the part of consuming regions. Habit formation can generate delayed responses (Pollack and Wales 1969). This is particularly true for wheat because an importer=s preference for a specific class of wheat depends on its end uses. This fact tends to freeze demand patterns in the short run because consumption of final goods and technological capabilities evolve fairly slowly so that there will be a tendency for limited responsiveness to short-run price variations. However, in a longer time frame, changes in final consumer demand and technological innovation could lead to shifts in importer preferences as millers discover ways to blend or enhance cheaper wheats to obtain the desired characteristics at lower cost. Millers in the EU have been able to concentrate protein and other desirable attributes in their relatively low-quality wheat, reducing the need to import North American wheat for blending (Leuck 1990). Another important reason for a slow response to price changes might be long-term trade agreements (LTA) between an importer and an exporter. LTAs typically involve shipments 5 periods of two or more seasons and often provide an upper and lower bound on purchases (Harwood and Bailey 1990). Thus, LTAs can decrease an importer=s flexibility to respond immediately to market conditions. LTAs are widely used in world wheat trade (Harwood and Bailey). In the 1980s, approximately 25 to 30 percent of world wheat was traded through LTAs (OECD 1987). Model Specification Based on the preceding discussion, a model that includes dynamic responses over more than one time period seems called for to represent the behavior of firms and consumers in the United States and the EU. This study uses a general dynamic demand framework extended to the AIDS system following the procedure of Wickens and Breusch (1988). A similar dynamic specification has been used by Kesavan, et al. (1993) to evaluate the dynamics and long-run structure of U.S. meat demand. The AIDS model seems to be the most robust choice of the many flexible demand systems available for specification in a dynamic setting (Anderson and Blundell 1983). The AIDS model is derived by specifying an expenditure function representing a PIGLOG class of preferences. This PIGLOG class of preference leads to the following cost function: log c (u, p) = (1-u) log a(p) + u log b (p), where the positive linearly homogeneous functions a (p) and b(p) may be regarded as the costs of subsistence and bliss. The functional forms for a (p) and b (p) are chosen such that the first PIGLOG is a special form of the price-independent, generalized (PIGL) class of preferences. 6 and second derivatives of the cost function can be set equal to those of an arbitrary cost function, thus satisfying the necessary condition for flexibility of functional form. The demand function is derived from the cost function using Shepherd=s lemma because of the fundamental property of the cost function that its price derivatives are the quantity demanded. Multiplying both sides of the first derivatives of the cost function by pi /c(u, p), the left-hand side may be expressed as a budget share and the right-hand side may be expressed as a function of prices and utility. The cost function is then solved for u and the resulting term is substituted for u in the budget share equation. Thus, we have budget shares as a function of p and M (total expenditures: where Wi, t is the budget share of the i th commodity, Pj is the price of the j th commodity, and M is the total budget outlay. P is the price index defined by The original price index (equation 2) is usually replaced by a Stone=s price index because of its nonlinearity. Use of the Stone=s price index allows for a linear estimation of the system. When the Stone price index is used in equation 1, the system is referred to as linear approximation of the Almost Ideal Demand System (LA/AIDS) (Blanciforti, et. al. 1986). In an application, Johnson (1983) suggested that use of Stone=s price index is a reasonably accurate approximation of Deaton and Muellbauer=s original price index. Stone=s price index is defined as the weighted average of prices by budget share and is defined as ), / ( + ) ( P M P + = W t t i jt ij n 1 = j i it ln ln β γ α ∑ Ln Ln Ln Ln i 0 j i i j j j (P) = + p p j ( ) + 1/2 ( ) (p ). γ α α ∑ ∑